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Applicability of (Ideal) Hydrodynamics to (Strangeness) RHIC Data (from an Experimentalist’s View)

Explore the applicability of ideal hydrodynamics to study strangeness in collisions using RHIC experimental data. Discussions include information obtained on the system, thermalization, final conditions, EoS, and space-time evolution. Analysis covers spectra, elliptic flow, and comparisons with data, aiming to understand the limitations and validity of the ideal assumption.

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Applicability of (Ideal) Hydrodynamics to (Strangeness) RHIC Data (from an Experimentalist’s View)

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  1. Strangeness in Collisions RIKEN-BNL Workshop, February 16-17, 2006 BNL Applicability of (Ideal) Hydrodynamics to (Strangeness) RHIC Data(from an Experimentalist’s View) • Ideal Hydrodynamics • Comparison with data • Spectra • Elliptic flow • Beyond Ideal Hydro • Summary, Conclusion and Open Questions Jeff Speltz Institut de Recherches Subatomiques, Strasbourg

  2. Ideal Fluid Dynamics • What information can we get on the system ? • Early, localthermalization? • QGP? (via the Equation of State: EoS, partonic dof) • Freeze-out conditions of the medium • What is the (important) input required? • Initial conditions : • At what time is the thermalization hypothesis valid (τ0)? • Space–time evolution of the system : • EoS: p = p(e,n) • Final conditions: • When is the thermalization hypothesis not valid anymore (Tdec)? • What does ideal assume ? • Micro p distribution is thermal in (r,t) • Mean Free Path λ≈ 0 • (Does not require chemical equilibrium : Tch) J. Speltz - RIKEN-BNL Workshop, BNL

  3. Hydrodynamical model results P.F. Kolb, J. Sollfrank and U.Heinz, Phys. Rev. C 62 (2000) 054909 P.F. Kolb and R. Rapp, Phys. Rev. C 67 (2003) 044903 P.F. Kolb and U.Heinz, nucl-th/0305084 … • (2+1) hydro (+ partial chemical equilibrium Tch ≈ 165 MeV) • P.F. Kolb, J. Sollfrank, U. Heinz, P. Huovinen, … • For most shown results • Full 3D hydro ( + cascade) • S.A. Bass, C. Nonaka, D. Teaney, J. Lauret, E.V. Shuryak, T. Hirano, M. Gyulassy, … • √sNN = 62.4 GeV results : (Preliminary !) • Using and tuning P.F. Kolb and U.Heinz model: • τ0( 62 GeV) = τ0 (200 GeV) = 0.6 fm/c ; s0 (62 GeV) < s0 (200 GeV) • EoS : 1st order phase transition at Tc. Tc = Tch = 165 MeV; different Tdec C. Nonaka and S.A Bass, nucl-th/0510038 D. Teaney et al., nucl-th/0110037 T. Hirano and M. Gyulassy, nucl-th/0506049 … http://nt3.phys.columbia.edu/OSCAR/models/list.html#AZHYDRO E. Frodermann and U. Heinz, private communication (2005) (s0 : initial (at τ0) entropy density) J. Speltz - RIKEN-BNL Workshop, BNL

  4. π-, K-, p : reasonable agreement Central Spectra : 200 GeV • Best agreement for : Tdec= 100 MeVα = 0.02 fm-1 • α≠ 0 : importance of inital conditions • Only at low pT (pT < 1.5 – 2 GeV/c) • Failing at higher pT (> 2 GeV/c) expected: • Less rescattering Central Data Tdec = 165 MeV Tdec = 100 MeV Thermalization validity limit P.F. Kolb and R. Rapp, Phys. Rev. C 67 (2003) 044903 α : initial (at τ0) transverse velocity : vT(r)=tanh(αr) J. Speltz - RIKEN-BNL Workshop, BNL

  5. π-, K-, p : apparent disagreement? Central Spectra : 62.4 GeV STAR preliminary data • Predictions normalized to data • Limited range of agreement • Hydro starts failing at 62 GeV? • different feed-down treatment in data and hydro? • Different initial / final conditions as at 200 GeV ? • Lower Tdec at 62 GeV ? • Larger τ0 at 62 GeV ? • Increasing τ0 gives much better agreement! • Tdec = 100 MeV J. Speltz - RIKEN-BNL Workshop, BNL

  6. pT = 2 GeV/c Strange Baryons Central Spectra : 62.4 GeV Λ spectra, central STAR preliminary • Small feed-down contribution • Hydro normalized to fit data (no μS) • Best reproduced with • Tdec ≈ 100 MeV • α ≠ 0 fm-1 • Same as for π-, K-, p • Tdec ≈ 164 MeV (decoupling at hadronization): not enough radial flow • True for all strange baryons! Ω- spectra, central Ξ- spectra, central STAR preliminary STAR preliminary τ0 = 0.6 fm/c mT – m0 (GeV/c2) mT – m0 (GeV/c2) J. Speltz - RIKEN-BNL Workshop, BNL

  7. pT = 2 GeV/c Ω- : best for Tdec = 100 MeV Central Spectra : 200 GeV • Only prediction for Ω- • Similar conclusion as 62 GeV • Tdec = 100 MeVbest fits data • Tdec (π, K, p ) ≈ Tdec(Ξ,Ω) (both energies) • But … Ξ,Ω • Supposed smaller cross-section • Less hadronic interactions than π, K ,p • T > 100 MeV (e.g. BW) • Inconsistency? Tdec = 165 MeV Tdec = 100 MeV Ω- spectra, central P.F. Kolb and U. Heinz, nucl-th/0305084 J. Speltz - RIKEN-BNL Workshop, BNL

  8. Blast-Wave Central Spectra E. Schnedermann et al., Phys. Rev. C 48 (1993) 2462 F. Retière and M. Lisa, Phys. Rev. C 70 (2004) 044907 • Blast-Wave: hydro inspired parameterization: • Parameter Tkin • Parameter <βT> • Direct fit (Χ2) on the data • Blast-Wave gives slightly different results than hydro : • Tkin~ Tch > 100 MeV • sensitivity on fit range and on the velocity profile? • Large errors • B-W fit on hydro : Tkin ≠ Tdec(up to 30 MeV difference) • Are Tdec and Tkin the same physical quantity? ~ 160 MeV ~ 125 MeV 100 MeV J. Speltz (for the STAR Collaboration), nucl-ex/0512037 J. Speltz - RIKEN-BNL Workshop, BNL

  9. Compilation of comparisons Central Spectra : 62.4 GeV • Use π, K, p B-W parameters onmulti-strange baryons • Tkin = 90 - 100 MeV • <βT> = 0.57 c • Ξ- and Ω- spectra not reproduced Differences between Ξ-, Ω- and π, K, p mainly due to <βT> (best constrained) J. Speltz (for the STAR Collaboration), nucl-ex/0512037 J. Speltz - RIKEN-BNL Workshop, BNL

  10. b (fm) 2.4 4.1 5.7 7.4 10.5 12.4 0 – 5 % 5 – 10 % 10 – 20 % 20 – 40 % 40 – 60 % 60 – 80 % pT = 2 GeV/c Strange Baryons Spectra, centrality dependence : 62.4 GeV central Λ • pT < 2 GeV/c : good agreement except for very peripheral collisions • Most peripheral not reproduced by hydro (what ever Tdec) • pT > 2 GeV/c : deviation larger for peripheral collisions than for central • τ0 = 0.8 fm/c : even better agreement STAR preliminary hydro Tdec = 100 MeV ; α = 0.02 fm-1 ; τ0 = 0.6 fm/c hydro Tdec = 100 MeV ; α = 0.02 fm-1 ; τ0 = 0.8 fm/c hydro Tdec = 164 MeV ; α = 0.02 fm-1 ; τ0 = 0.6 fm/c peripheral Ξ- Ω- STAR preliminary STAR preliminary Scaling factors applied for better viewing J. Speltz - RIKEN-BNL Workshop, BNL

  11. Tdec = 100 MeV π+ spectra Tdec = 100 MeV proton spectra Thermalization hypothesis less valid with less centrality π+, p Spectra, centrality dependence : 200 GeV • No comparison available for strange baryons • Ideal hydro fails at smaller pT for more peripheral collisions • Basically same results as at 62 GeV P.F. Kolb and R. Rapp, Phys. Rev. C 67 (2003) 044903 • Failing at higher-pT (> 2 GeV) and peripheral collisions expected: • Less rescattering • Smaller system size Central : b = 2.4 fm Semi-central : b = 7 fm Peripheral : b = 9.6 fm J. Speltz - RIKEN-BNL Workshop, BNL

  12. Hydro features Elliptic flow : 200 GeV • Mass hierachy at low pT from hydro in data • Agreement until pT~ 2 GeV/c • Same as for spectra • pT > 2 GeV/c data deviates from hydro • Describtion possible with dissipative effects interactions Anisotropy in momentum v2 Anisotropy in space Self-quenching : Sensitive to early stage of the evolution Anisotropy parameter v2 J. Adams et al., Phys. Rev. C 72 (2005) 014904 D. Molnar and M. Gyulassy, Nucl. Phys. A 697 (2002) 495 Early thermalization : account for large v2 J. Speltz - RIKEN-BNL Workshop, BNL

  13. Flow of s quark Elliptic flow : 200 GeV • All strange particles (including Ω(sss) and φ(ss)) flow (s quark flow as large as for light quarks) • Further indication for thermalization • Indication for collective flow in partonic phase (small hadronic cross-section for Ω,φ, meson/baryon difference) STAR preliminary Hydro: P. Huovinen, private communication M. Oldenburg, QM 2005 J. Speltz - RIKEN-BNL Workshop, BNL

  14. Hydro features Elliptic flow : 62.4 GeV Preliminary • No “real” min-bias measurement • Same features as at 200 GeV: • Mass hierachy • Breakdown at pT~ 2 GeV/c • s quark flow • Same parameters as for spectra • α ≠ 0 • Tdec ≈ 100 MeV • τ0 doesn’t change the conclusion dramatically STAR preliminary J. Speltz - RIKEN-BNL Workshop, BNL

  15. v2 : Centrality and Rapidity dependence Beyond Ideal Hydro To Get the η dependence : 3D model • All results shown so far are from (2+1) hydro calculations P.F. Kolb et al., Nucl. Phys. A 696 (2001) 197 T. Hirano and M. Gyulassy, nucl-th/0506049 T. Hirano, nucl-th/0601006 Assuming thermalization generates too much flow: remedy = cascade J. Speltz - RIKEN-BNL Workshop, BNL

  16. Extending the view: hydro + cascade Beyond Ideal Hydro hybrid • Thermalization, perfect fluidity (hydro) in the sQGP phase • At Tch ≈ Tc : microscopic hadron/parton cascade model (RQMD, UrQMD,…), accounts for viscosity and dissipative effects in the hadronic phase π Hydro + RQMD C. Nonaka and S.A. Bass, nucl-th/0510038 D. Teaney et al., nucl-th/0110037 • No Strangeness Yet: • Spectra: data available; need prediction • d2v2/dpTdNch: results not yet available J. Speltz - RIKEN-BNL Workshop, BNL

  17. CGC+Hydro+Cascade Beyond Ideal Hydro • Full description: modeling also the period beforethermalization: CGC, e-by-e fluctuations (Nexus),… • CGC+hydro+cascade gives a good describtion of dv2/dη data • Strangeness: • Data : Weak decay reconstruction at finite η challenging! h± T. Hirano and M. Gyulassy, nucl-th/0506049 T. Hirano, nucl-th/0601006 J. Speltz - RIKEN-BNL Workshop, BNL

  18. Incomplete Thermalization? Beyond Ideal Hydro • Most models (also hybrids) assume ideal hydro at some point • Ideal Hydro predictions not seen in data: • v4/v22 = 1/2 in ideal hydro (data v4 > v22/2) • v2 /ε (1/S dNch/dy) = cte. N. Borghini, nucl-th/0509092 N. Borghini and J.-Y. Ollitrault, nucl-th/0506045 R.S. Bhalerao et al., Phys. Lett. B 627 (2005) 49 v4/v22 J. Adams et al., Phys. Rev. C 72 (2005) 014904 C. Alt et al., Phys. Rev. C 68 (2003) 034903 More precise mesurements to come (including strangeness) J. Speltz - RIKEN-BNL Workshop, BNL

  19. Conclusion/Summary and open questions • Ideal hydro gives goodagreement with (strangeness) data: • Spectra and Elliptic flow at all RHIC energies (62 GeV to 200 GeV) • EoS including phase transition gives nice accord • Indication for (early) thermalization • Kinetic Freeze-out (Tdec) similar for all particles • clarify on Blast-Wave (more precise measurement, Alice…) • Ω : Mass evolution and test full equilibrium of all light flavors • Interplay of τ0, α and Tdec: is it really understood? (Indications that τ0(62 GeV) > τ0(200GeV) ) • Importance of 62.4 GeV! Possible insight to hydro breakdown • Nothing is really perfect (ideal): • but closest to perfect we have ever seen • Breakdown : hybrid models, viscosity • Test these tools on strangeness J. Speltz - RIKEN-BNL Workshop, BNL

  20. STAR preliminary Mean pT Centrality dependence • Central : Good agreement of <pT> for most particules • Peripheral : <pT> not reproduced • As spectra is not reproduced il y a un double aspect dans la comparaison. Rappelles-toi que Nu vois des courbes "plates" pour les "multi-stranges" comparées aux autres espèces légères... Peut-on lier cette observation au fait que l'hydro fail ??? (à mon avis c'est difficile, mais il faut être conscient de ce pb) P.F. Kolb and U. Heinz, nucl-th/0305084 T. Chujo et al., Nucl. Phys. A 715 (2003) 151 • 62 GeV and 200 GeV results similar Hydro: Tdec = 100 MeV τ0 = 0.6 fm/c J. Speltz - RIKEN-BNL Workshop, BNL

  21. Viscosity Beyond Ideal Hydro • If only small deviations from ideal (non-viscous) behaviour : viscous relativistic hydrodynamics η : shear viscosity s : entropy density Γs/τ~ 0.1 => η/s ~ limit P. Kovtun et al., hep-th/0405231 As η~ 0.1 GeV/fm2 around Tc in QGP and hadronic phase, but η/s large in HG => sudden reduction of s => deconfinement T. Hirano and M. Gyulassy, nucl-th/0506049 and D. Teaney, Phys. Rev. C 68 (2003) 034913 Use of EoS including QGP gives best results with data U. Heinz and P. Kolb, hep-ph/0204061 J. Speltz - RIKEN-BNL Workshop, BNL

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